HYPOTHESIS AND THEORY article
Front. Appl. Math. Stat.
Sec. Mathematical Biology
Volume 11 - 2025 | doi: 10.3389/fams.2025.1523276
This article is part of the Research TopicModeling Ecological and Epidemiological Interactions for Sustainable PracticesView all 6 articles
Dynamic Complexity of a Delayed Spatiotemporal Predator-Prey Model
Provisionally accepted
- 1University of Hassan II Casablanca, Casablanca, Morocco
- 2National School of Applied Sciences of Marrakech, Cadi Ayyad University, Marrakech, Morocco
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This study investigates a delayed spatiotemporal predator-prey model that incorporates key ecological mechanisms, including the Allee effect, fear-induced prey behavior, Holling type II predation with cooperative hunting, toxicity with delayed effects, and both nonlinear (for prey) and linear (for predators) fishing pressures. Using tools from the theory of partial differential equations, stability analysis, and Hopf bifurcation theory, we derive the conditions under which stable coexistence or instability emerges. Our results reveal that system stability is maintained below a critical delay threshold, beyond which oscillatory dynamics arise. In the spatial domain, diffusion can either stabilize populations or lead to heterogeneous patterns such as Turing structures and predator-prey segregation, particularly when diffusion is low and delays are significant. Numerical simulations support and illustrate the analytical findings, showing a variety of dynamic behaviors consistent with observed ecological patterns. This work highlights how the interplay between ecological processes, time delays, and spatial effects governs predator-prey dynamics and offers insights relevant to ecosystem management.
Keywords: Diffusion, Prey-predator, stability analysis, Delay, Hopf bifurcation, Turing instability
Received: 05 Nov 2024; Accepted: 26 May 2025.
Copyright: © 2025 HAFDANE, Baba, EL FOUTAYENI and ACHTAICH. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Mohamed HAFDANE, University of Hassan II Casablanca, Casablanca, Morocco
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